2026/061) Five distinct 2-digit numbers are in a geometric progression. Find the middle term.

Without loss of generality we can assume that nmbers are in increasing sequence 

We have 3 powers of 2 as 2 digit numbers . They are 16,32,64. 

If we start at 10 we get 4 numbers in geometric progression when ratio is 2. 

So we need some ratio less than 2 . Common ratio can be fraction as long as we do not get a fraction after multiplying by common ratio . 

Because we need 5 numbers we need to multiply 4 times . So we start with a 4th power of 2 that is 16 and common ratio $\frac{3}{2}$ 16 giving 16, 24,36,54,81 and middle term is 36.

Basically  5 numbers $a^4,a^3b,a^2b^2,ab^3,b^4$ where a is starting number and $\frac{b}{a}$ as common ratio. form  GP.